Skip to main content
SpringerLink
Log in

Non-minimal Degree-Sequence-Forcing Triples

  • Original Paper
  • Published:
Graphs and Combinatorics Aims and scope Submit manuscript

Abstract

Given a set \(\mathcal {F}\) of graphs, a graph \(G\) is \(\mathcal {F}\)-free if \(G\) does not contain any member of \(\mathcal {F}\) as an induced subgraph. We say that \(\mathcal {F}\) is a degree-sequence-forcing set if, for each graph \(G\) in the class \(\mathcal {C}\) of \(\mathcal {F}\)-free graphs, every realization of the degree sequence of \(G\) is also in \(\mathcal {C}\). A degree-sequence-forcing set is minimal if no proper subset is degree-sequence-forcing. We characterize the non-minimal degree-sequence-forcing sets \(\mathcal {F}\) when \(\mathcal {F}\) has size \(3\).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

References

  1. Barrus, M.D., Kumbhat, M., Hartke, S.G.: Graph classes characterized both by forbidden subgraphs and degree sequences. J. Graph Theory 57(2), 131–148 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  2. Barrus, M.D., Hartke S.G.: Minimal forbidden sets for degree sequence characterizations (submitted)

  3. Blázsik, Z., Hujter, M., Pluhár, A., Tuza, Z.: Graphs with no induced \(C_{4}\) and \(2K_{2}\). Discrete Math. 115(1–3), 51–55 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  4. Chudnovsky, M., Robertson, N., Seymour, P.D., Thomas, R.: The strong perfect graph theorem. Ann. Math. (2) 164(1), 51–229 (2006)

  5. Chvátal, V., Hammer, P.L.: Aggregation of inequalities in integer programming. In: Hammer, P.L., Johnson, E.L., Korte, B.H., Nemhauser, G.L. (eds.) Studies in Integer Programming, pp. 145–162. North-Holland, New York (1977)

    Chapter  Google Scholar 

  6. Faudree, R.J., Gould, R.J., Jacobson, M.S., Lesniak, L.L.: Characterizing forbidden clawless triples implying Hamiltonian graphs. Discrete Math. 249(1–3), 71–81 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  7. Faudree, R.J., Gould, R.J., Jacobson, M.S.: Forbidden triples implying hamiltonicity: for all graphs. Discuss. Math. Graph Theory 24(1), 47–54 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  8. Földes, S., Hammer, P.L.: On split graphs and some related questions. In: Problèmes Combinatoires et Théorie Des Graphes, pp. 138–140. Colloques internationaux C.N.R.S. 260, Orsay (1976)

  9. Fulkerson, D.R., Hoffman, A.J., McAndrew, M.H.: Some properties of graphs with multiple edges. Can. J. Math. 17, 166–177 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  10. Gould, R.J., Łuczak, T., Pfender, F.: Pancyclity of 3-connected graphs: pairs of forbidden subgraphs. J. Graph Theory 47(3), 183–202 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  11. Hammer, P.L., Ibaraki, T., Simeone, B.: Degree sequences of threshold graphs. In: Proceedings of the Ninth Southeastern Conference on Combinatorics, Graph Theory, and Computing, pp. 329–355. Florida Atlantic Univ., Boca Raton, Fla., 1978. Congress. Numer., XXI, Utilitas Math., Winnipeg, Man (1978)

  12. Hammer, P.L., Simeone, B.: The splittance of a graph. Combinatorica 1, 275–284 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  13. Kleitman, D.J., Li, S.-Y.: A note on unigraphic sequences. Stud. Appl. Math. 54(4), 283–287 (1975)

    MathSciNet  MATH  Google Scholar 

  14. Maffray, F., Preissmann, M.: Linear recognition of pseudo-split graphs. Discrete Appl. Math. 52, 307–312 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  15. Randerath, B.: 3-colorability and forbidden subgraphs. I. Characterizing pairs. Discrete Math. 276(1–3), 313–325 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  16. West, D.B.: Introduction to Graph Theory. Prentice Hall Inc, Upper Saddle River (1996)

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Brigham Young University, Provo, UT, 84602, USA

    Michael D. Barrus

  2. Department of Mathematics, University of Nebraska, Lincoln, NE, 68588-0130, USA

    Stephen G. Hartke

  3. Department of Mathematics, Sungkyunkwan University, Suwon, 440746, South Korea

    Mohit Kumbhat

Authors
  1. Michael D. Barrus
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Stephen G. Hartke
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mohit Kumbhat
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohit Kumbhat.

Additional information

Research partially supported by a Maude Hammond Fling Faculty Research Fellowship from the University of Nebraska Research Council, a Nebraska EPSCoR First Award, and National Science Foundation Grant DMS-0914815.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Barrus, M.D., Hartke, S.G. & Kumbhat, M. Non-minimal Degree-Sequence-Forcing Triples. Graphs and Combinatorics 31, 1189–1209 (2015). https://doi.org/10.1007/s00373-014-1450-0

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00373-014-1450-0

Keywords

Mathematics Subject Classification (2000)

Search

Navigation